# Cover E -> B gives a homeomorphism E/Aut(E) -> B

Let $p : E \rightarrow B$ be a cover s.t. Aut(E) acts transitively on $p^{-1}(b)$ for some fix $b \in B$. Then $E/Aut(E)$ is homeomorphic to $B$ where $Aut(E) \subset Cov(E,E)$. The problem is that I don't even understand how the map E/Aut(E) -> B is defined, would someone please give me this definition? Apparently it is "clear" but I fail to see this.

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$\widetilde{x} \mapsto p(x)$? (Where $\widetilde{x}$ is the class of $x$ in $E/\!\mathrm{Aut}(E)$.) –  a.r. Sep 17 '10 at 13:20
Thank you, I feel ashamed... –  Down Sep 23 '10 at 15:04

Let's remove this question from the list of unanswered questions by up-voting this community wiki answer stating that Agusti Roig's comment above contains the right answer.

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Let's honor Rasmus' creative handling of the software restrictions by downvoting this self-referential community wiki answer.

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Funny, for a moment I thought you got this idea from mathoverflow.net/questions/39626/… but apparently that post turned up later. –  Rasmus Sep 22 '10 at 17:31